It's also very normal for your kitten to want to play. Play-fighting is essential for kittens; it's how they learn to take care of themselves when they are older, and you'll see kittens in a litter engaging in this activity as soon as they are aware of each other.
For these reasons, I always suggest using care when bringing a new cat into a home. Under the present circumstances, it is unlikely that your two cats will be able to peacefully co-exist until the kitten is much older. In the meantime, the intrusion is unsettling to the adult, who was after all, there first. You originally had no choice, of course, since the kitten obviously needed a home when you rescued him.
As I see it, you presently have two options:
- Find a new home for the kitten, either one with other kittens, or one where he will be the only cat.
- Adopt another kitten, so your young guy can get the exercise and play he needs, without bothering the adult.
The second option was my thought when I launched "the great kitten search" five years ago. The death of our 19 year old Shannon left us with only one cat, Bubba, who was also in advanced years. I really wanted another red cat because we'd always had at least one of them, and I was afraid that Bubba would not accept an older cat. Because I knew that a kitten would also be too much for him, for the very reasons you've outlined, my reasoning was that two kittens would provide them with a play companion, and they'd leave Bubba alone. It worked out perfectly, and to my surprise, Bubba became very fond of Jaspurr, the red kitten.
Your third alternative would be to try to personally give your six-month-old plenty of play opportunities, with interactive toys such as wands, in the hopes that he would ease up on your poor adult cat. It could work, at least to buy enough time for the youngster to mature and settle down. But the bottom line is that only you know your two cats well enough to decide which course to take.